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Generalized Coupled Thermoplasticity Taking into Account Large Strains: Part I. Conditions of Uniqueness of the Solution of Boundary-Value Problem and Bifurcation Criteria

Faculty of Applications of Chemistry and Mechanics, Opole University of Technology, Luboszycka 5, 45-036 Opole, Poland

^* To whom correspondence should be addressed.

	Abstract

The global and local conditions of uniqueness and the criteria excluding a possibility of bifurcation of the equilibrium state for large and small strains are derived. The conditions and criteria are derived analyzing the problem of uniqueness of solution of the basic incremental boundary problem of coupled generalized thermoplasticity. This paper is a continuation of some previous work, but contains new derivation of the global and local criteria excluding a possibility of bifurcation of the equilibrium state for a comparison body dependent on statically admissible fields of stress velocity. All the thermomechanical coupling effects, non-associated laws of plastic flow and influence of plastic strains on thermoplastic properties of a body were taken into account in this work. Thus, the mathematical problem considered here is not a self-conjugated problem.

Key Words: Bifurcation of the equilibrium state, conditions and criteria of uniqueness, boundary-value problem, generalized coupled thermoplasticity, comparison body

First published on March 11, 2009
Mathematics and Mechanics of Solids 2009, doi:10.1177/1081286508100730


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